Document Sample

```					Audit Sampling

CELT
October 2004
Statistics as an Audit Tool

• Auditors use inferential statistics to draw
conclusions about populations based on samples
of data.

• Why do auditors use samples—usually too costly
and time-consuming to examine entire ―universe‖
Sampling Techniques

• Sampling techniques include:
– Judgment sampling: subjective selection of
sample size and items (target high-risk
transactions)
– Statistical sampling techniques:
• Random sampling: each item has equal
probability
• Block sampling: randomly selected clusters
• Systematic sampling: random start and then
take every nth item
Audit Sampling and Tests

• Substantive testing and variables sampling—
selecting samples of values measuring quantifiable
magnitudes (e.g., costs, number of units sold)

• Tests of controls and attributes sampling—
selecting sample of transactions from data
population to test for presence or absence of
certain qualities.
Materiality and Precision

• Materiality and precision are related concepts that
also affect sample size.
• Materiality—a 10 percent misstatement in the
accounts receivable balance is probably material;
but a 10 percent misstatement in the office
supplies account balance might not be.
• If testing accounts receivable balances, we’ll need
to look at a larger sample if we want to have an
estimate that falls within 10 percent, than if our
desired precision was only 20 percent.
Confidence

• Confidence is also important in determining
sample size.
• The greater the confidence, the larger the sample
size.
• So if we want to be 95 percent confident that the
estimated accounts receivable balance falls within
10 percent of the true value, we will need a larger
sample than if we only needed to be 80 percent
confident.
Calculating Precision
(Variable Sampling)
• Calculating precision—need to know:

(1) Standard deviation (a measure of how much
variability there is in the population)
(2) The t-value associated with the desired level of
confidence, and
(3) A proposed sample size.
Calculating Precision (continued)

(1) Standard deviation is a measure of how much
variability there is in the population of data.
 (x – x )2
(n – 1)
• x is the value of the sampling unit, x is the
mean (average), and n is the sample size
• Standard deviation can be calculated in
Excel—―STDEV‖
Calculating Precision (continued)

(2) t-values are multipliers based on level of
confidence—any standard statistics textbook will
have a table of t-values.
• A commonly used confidence level is 95
percent, which has an associated t-value of
1.96.
(3) In our example, assume we’re looking at
accounts receivable balances and we’re using a
sample of 30 balances. Our sample size (n) is 30.
Calculating Precision (continued)

• Sampling Error of the Mean =         t * SD
n
• t = 1.96, SD = 48.71, and n = 30

• Sampling Error (or precision) = \$17.43.

• If we assume that there are 100 transactions in the
population, we can be 95 percent confident that
our estimate of the total value is within \$1,743 of
the true value.
Calculating Sample Size
(Variable Sampling)
• Assume we want better precision—we want our
estimate to fall within \$1,400 of the true total.
• n = t 2 * SD 2
(E)2
• Again, t = 1.96, SD = 48.71, E (or Error) =
\$14
• n = 47
Determining Confidence Interval for
Proportion (Attribute Sampling)
• Calculate the percentage of the sample that has the
attribute (e.g., 12 of 40 approval forms were not
signed properly = 30 percent).
• For 95 percent confidence: Multiply 1.96 by
Standard Error of the Proportion and add to and
subtract from 30 percent to get high and low end
of interval.
Standard Error of the Proportion

• SE = p * (1 – p)
n

• Where p is the proportion (or 30 percent in our
example), 1 – p = 70 percent, and n is the sample
size (or 40).

• Standard Error in this example = 0.072
Confidence Interval for Proportion

• So we add (1.96 * 0.072) to 0.30 to get high end
of 95 percent confidence interval, and subtract
same amount from 0.30 to get low end.
• Confidence interval is from 0.16 to 0.44.
• In plain English, this means that we can be 95
percent confident that the proportion of all
approval forms that were not properly signed falls
between these two values.
Calculating Sample Size
(Attribute Sampling)
• n = (1.96)2 * p * (1 – p)
E2
• Again, n is the sample size and p is the proportion
• E is the level of precision—i.e., do we want to be
within 2 percent or within 5 percent of the true
proportion?
• If we want to be 95 percent confident our estimate
falls within 5 percent, the sample size would have
to be 323.
General Tips:
Planning the Analysis
• Conduct pre-sampling research to better
understand the process being tested—interview
audit clients and others involved in the process
and document system controls
• Define the objective so results will add value
• Define the population—what is the population you
want to draw conclusions about (e.g., what time
period, what range of dollar values, etc.)
General Tips:
Conducting the Analysis
• Determine level of acceptable risk and calculate
sample size—sample size will depend on
population size, acceptable risk, variability in
population, and tolerable misstatement/deviation
from what is expected
• Review the sample—identify deviations from
prescribed control in test of controls, or use
descriptive statistics for substantive testing
• Document, document, document! Document
sampling methodology, calculations, and results

• US General Accountability Office, ―Using
Statistical Sampling,‖ May 1992.

• General Statistics Information:
http://www.go2hill.com/ResearchDevelopment/St
atistics/zd_ebstat.htm or
http://edis.ifas.ufl.edu/PD006

• Random number generator:
http://www.random.org/

```
DOCUMENT INFO
Shared By:
Categories:
Stats:
 views: 110 posted: 7/6/2010 language: English pages: 18
Description: Calculate Error Percentage document sample
How are you planning on using Docstoc?